Finding vector magnitude and direction from vector components (3-2)

Question 1 of 4

Question

Magnitude of the vector $\boldsymbol{\vec{A}}$

{"title":"magnitude of the vector A","description":"Correct","type":"correct","color":"#99CCFF","code":"[{\"shape\":\"rect\",\"coords\":\"24,18,47,45\"}]"} {"title":"x component of the vector A","description":"Wrong","type":"incorrect","color":"#ffcc00","code":"[{\"shape\":\"rect\",\"coords\":\"73,22,92,43\"},{\"shape\":\"rect\",\"coords\":\"275,30,299,49\"}]"} {"title":"y component of the vector A","description":"Incorrect","type":"incorrect","color":"#333300","code":"[{\"shape\":\"rect\",\"coords\":\"122,22,147,43\"},{\"shape\":\"rect\",\"coords\":\"277,1,298,29\"}]"} {"title":"angle of the vector A measured from the positive x axis toward the positive y axis","description":"Incorrect","type":"incorrect","color":"#000080","code":"[{\"shape\":\"rect\",\"coords\":\"238,15,262,38\"}]"}

Question

$x$ component of the vector $\boldsymbol{\vec{A}}$

{"title":"magnitude of the vector A","description":"Incorrect","type":"incorrect","color":"#99CCFF","code":"[{\"shape\":\"rect\",\"coords\":\"24,18,47,45\"}]"} {"title":"x component of the vector A","description":"Correct","type":"correct","color":"#ffcc00","code":"[{\"shape\":\"rect\",\"coords\":\"73,22,92,43\"},{\"shape\":\"rect\",\"coords\":\"275,30,299,49\"}]"} {"title":"y component of the vector A","description":"Incorrect","type":"incorrect","color":"#333300","code":"[{\"shape\":\"rect\",\"coords\":\"122,22,147,43\"},{\"shape\":\"rect\",\"coords\":\"277,1,298,29\"}]"} {"title":"angle of the vector A measured from the positive x axis toward the positive y axis","description":"Incorrect","type":"incorrect","color":"#000080","code":"[{\"shape\":\"rect\",\"coords\":\"238,15,262,38\"}]"}

Question

Angle of the vector $\boldsymbol{\vec{A}}$ measured from the positive $x$ axis toward the positive $y$ axis

{"title":"magnitude of the vector A","description":"Incorrect","type":"incorrect","color":"#99CCFF","code":"[{\"shape\":\"rect\",\"coords\":\"24,18,47,45\"}]"} {"title":"x component of the vector A","description":"Incorrect","type":"incorrect","color":"#ffcc00","code":"[{\"shape\":\"rect\",\"coords\":\"73,22,92,43\"},{\"shape\":\"rect\",\"coords\":\"275,30,299,49\"}]"} {"title":"y component of the vector A","description":"Incorrect","type":"incorrect","color":"#333300","code":"[{\"shape\":\"rect\",\"coords\":\"122,22,147,43\"},{\"shape\":\"rect\",\"coords\":\"277,1,298,29\"}]"} {"title":"angle of the vector A measured from the positive x axis toward the positive y axis","description":"Correct!","type":"correct","color":"#000080","code":"[{\"shape\":\"rect\",\"coords\":\"238,15,262,38\"}]"}

Question

$y$ component of the vector $\boldsymbol{\vec{A}}$

{"title":"magnitude of the vector A","description":"Incorrect","type":"incorrect","color":"#99CCFF","code":"[{\"shape\":\"rect\",\"coords\":\"24,18,47,45\"}]"} {"title":"x component of the vector A","description":"Incorrect","type":"incorrect","color":"#ffcc00","code":"[{\"shape\":\"rect\",\"coords\":\"73,22,92,43\"},{\"shape\":\"rect\",\"coords\":\"275,30,299,49\"}]"} {"title":"y component of the vector A","description":"Correct!","type":"correct","color":"#333300","code":"[{\"shape\":\"rect\",\"coords\":\"122,22,147,43\"},{\"shape\":\"rect\",\"coords\":\"277,1,298,29\"}]"} {"title":"angle of the vector A measured from the positive x axis toward the positive y axis","description":"Incorrect","type":"incorrect","color":"#000080","code":"[{\"shape\":\"rect\",\"coords\":\"238,15,262,38\"}]"}

Review

Once you have stated the $x$ component and $y$ component of a vector, you have defined the vector completely. So you can describe a vector such as $\vec{A}$ in terms of either (1) its magnitude $A$ and the angle $\theta$ or (2) its components $A_x$ and $A_y$ .